Question

Transverse waves travel with a speed of $40\text{m/s}$ in a string under a tension of $12\text{N}$. What tension is required for a wave speed of $60\text{m/s}$ in the same string?

• A. $25\text{N}$
• B. $29\text{N}$
• C. $27\text{N}$
• D. $21\text{N}$

Answer 1

The correct option is C $27\text{N}$

Transverse wave speed can be written as
$v_1=\sqrt{\frac{T_1}{\mu }}$ and $v_2=\sqrt{\frac{T_2}{\mu }}$
[$\mu$ will be same as the wire considered is same]
So,
$\frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}\Rightarrow T_2=T_1\times {\left(\frac{v_2}{v_1}\right)}^2$
From the data given in the question ,
$T_2=12\times {\left(\frac{60}{40}\right)}^2=12\times \frac{9}{4}=27\text{N}$
Thus, option (c) is the correct answer.